y=√2sin(2x+π/4)-1/2cos²x 化简~急用~
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y=√2sin(2x+π/4)-1/2cos²x 化简~急用~
![y=√2sin(2x+π/4)-1/2cos²x 化简~急用~](/uploads/image/z/16962047-71-7.jpg?t=y%3D%E2%88%9A2sin%282x%2B%CF%80%EF%BC%8F4%29-1%2F2cos%26%23178%3Bx+%E5%8C%96%E7%AE%80%7E%E6%80%A5%E7%94%A8%7E)
y=√2sin(2x+π/4)-1/2cos²x
=√2[sin(2x)cos(π/4)+cos(2x)sin(π/4)]-1/2cos²x
=√2[sin(2x)·√2/2+cos(2x)·√2/2]-1/2·(cos2x-1)/2
=[sin(2x)+cos(2x)]-1/4·cos2x+1/4
=sin(2x)+3/4·cos(2x)+1/4
=√[1²+(3/4)²]sin(2x+φ) (辅助角公式)
=5/4·sin(2x+φ)
=√2[sin(2x)cos(π/4)+cos(2x)sin(π/4)]-1/2cos²x
=√2[sin(2x)·√2/2+cos(2x)·√2/2]-1/2·(cos2x-1)/2
=[sin(2x)+cos(2x)]-1/4·cos2x+1/4
=sin(2x)+3/4·cos(2x)+1/4
=√[1²+(3/4)²]sin(2x+φ) (辅助角公式)
=5/4·sin(2x+φ)
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